The objective of this continuing project is to develop new-methods in statistics, using algebraic techniques, that have applications for biomedical research. Newly developed methods in variance component estimation, and estimation in models with linear covariance structure, were previously brought together and published in a book on the subject. Research on these methods continues, particularly with respect to applications in genetics, and animal sciences. The algebraic methods themselves continue to be studied with one paper being published in the past year, while another is accepted for publication. Further studies concern the use of Jordan algebras to solve the problem of estimation in the presence of missing data in the mixed linear model. This technique applies to repeated measures problems and longitudinal studies, both of much interest to the biomedical community.